2,350 results match your criteria Algebra Universalis[Journal]

Sparse Angle CBCT Reconstruction Based on Guided Image Filtering.

Front Oncol 2022 27;12:832037. Epub 2022 Apr 27.

Laboratoire d'Informatique, de Robotique et de Microélectronique de Montpellier (LIRMM), Unité Mixte de Recherche (UMR) 5506, French National Center for Scientific Research (CNRS) - University of Montpellier (UM), Montpellier, France.

Cone-beam Computerized Tomography (CBCT) has the advantages of high ray utilization and detection efficiency, short scan time, high spatial and isotropic resolution. However, the X-rays emitted by CBCT examination are harmful to the human body, so reducing the radiation dose without damaging the reconstruction quality is the key to the reconstruction of CBCT. In this paper, we propose a sparse angle CBCT reconstruction algorithm based on Guided Image FilteringGIF, which combines the classic Simultaneous Algebra Reconstruction Technique(SART) and the Total p-Variation (TpV) minimization. Read More

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Quantum Relativity of Subsystems.

Phys Rev Lett 2022 Apr;128(17):170401

Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755, USA.

One of the most basic notions in physics is the partitioning of a system into subsystems and the study of correlations among its parts. In this Letter, we explore this notion in the context of quantum reference frame (QRF) covariance, in which this partitioning is subject to a symmetry constraint. We demonstrate that different reference frame perspectives induce different sets of subsystem observable algebras, which leads to a gauge-invariant, frame-dependent notion of subsystems and entanglement. Read More

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Fluorescence Lifetime Phasor Analysis of the Decamer-Dimer Equilibrium of Human Peroxiredoxin 1.

Int J Mol Sci 2022 May 9;23(9). Epub 2022 May 9.

Laboratorio de Fisicoquímica Biológica, Instituto de Química Biológica, Facultad de Ciencias, Universidad de la República, Montevideo 11400, Uruguay.

Protein self-assembly is a common feature in biology and is often required for a myriad of fundamental processes, such as enzyme activity, signal transduction, and transport of solutes across membranes, among others. There are several techniques to find and assess homo-oligomer formation in proteins. Naturally, all these methods have their limitations, meaning that at least two or more different approaches are needed to characterize a case study. Read More

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Modular Structure of the Weyl Algebra.

Roberto Longo

Commun Math Phys 2022 19;392(1):145-183. Epub 2022 Mar 19.

Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, 1, 00133 Rome, Italy.

We study the modular Hamiltonian associated with a Gaussian state on the Weyl algebra. We obtain necessary/sufficient criteria for the local equivalence of Gaussian states, independently of the classical results by Araki and Yamagami, Van Daele, Holevo. We also present a criterion for a Bogoliubov automorphism to be weakly inner in the GNS representation. Read More

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Encouraging research on recursive thinking through the lens of a model of the spread of contagious diseases.

ZDM 2022 May 3:1-13. Epub 2022 May 3.

University of California San Diego, La Jolla, CA USA.

Recursive reasoning is a powerful tool used extensively in problem solving. For us, recursive reasoning includes iteration, sequences, difference equations, discrete dynamical systems, pattern identification, and mathematical induction; all of these can represent how things change, but in discrete jumps. Given the school mathematics curriculum's later emphasis on calculus-the mathematics of change in continuous contexts-it is surprising that the curriculum seems to neglect recursive thinking after the early grades. Read More

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On the role of continuous symmetries in the solution of the three-dimensional Euler fluid equations and related models.

Philos Trans A Math Phys Eng Sci 2022 Jun 9;380(2226):20210050. Epub 2022 May 9.

School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland.

We review and apply the continuous symmetry approach to find the solution of the three-dimensional Euler fluid equations in several instances of interest, via the construction of constants of motion and infinitesimal symmetries, without recourse to Noether's theorem. We show that the vorticity field is a symmetry of the flow, so if the flow admits another symmetry then a Lie algebra of new symmetries can be constructed. For steady Euler flows this leads directly to the distinction of (non-)Beltrami flows: an example is given where the topology of the spatial manifold determines whether extra symmetries can be constructed. Read More

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Electronic energies from coupled fermionic "Zombie" states' imaginary time evolution.

J Chem Phys 2022 May;156(17):174116

School of Chemistry, University of Leeds, Leeds LS2 9JT, United Kingdom.

Zombie states are a recently introduced formalism to describe coupled coherent fermionic states that address the fermionic sign problem in a computationally tractable manner. Previously, it has been shown that Zombie states with fractional occupations of spin orbitals obeyed the correct fermionic creation and annihilation algebra and presented results for real-time evolution [D. V. Read More

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A new algebraic approach to genome rearrangement models.

J Math Biol 2022 May 5;84(6):49. Epub 2022 May 5.

Discipline of Mathematics, School of Natural Sciences, University of Tasmania, Private Bag 37, Sandy Bay, TAS, 7001, Australia.

We present a unified framework for modelling genomes and their rearrangements in a genome algebra, as elements that simultaneously incorporate all physical symmetries. Building on previous work utilising the group algebra of the symmetric group, we explicitly construct the genome algebra for the case of unsigned circular genomes with dihedral symmetry and show that the maximum likelihood estimate (MLE) of genome rearrangement distance can be validly and more efficiently performed in this setting. We then construct the genome algebra for a more general case, that is, for genomes that may be represented by elements of an arbitrary group and symmetry group, and show that the MLE computations can be performed entirely within this framework. Read More

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Bond topology of chain, ribbon and tube silicates. Part I. Graph-theory generation of infinite one-dimensional arrangements of (TO) tetrahedra.

Acta Crystallogr A Found Adv 2022 May 4;78(Pt 3):212-233. Epub 2022 Apr 4.

Department of Earth Sciences, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada.

Chain, ribbon and tube silicates are based on one-dimensional polymerizations of (TO) tetrahedra, where T = Si plus P, V, As, Al, Fe and B. Such polymerizations may be represented by infinite graphs (designated chain graphs) in which vertices represent tetrahedra and edges represent linkages between tetrahedra. The valence-sum rule of bond-valence theory limits the maximum degree of any vertex to 4 and the number of edges linking two vertices to 1 (corner-sharing tetrahedra). Read More

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Online Strategies To Improve Quantitative Skills in Microbiology Laboratory Classes.

J Microbiol Biol Educ 2022 Apr 28;23(1). Epub 2022 Mar 28.

Department of Biology, Virginia Commonwealth University, Richmond, Virginia, USA.

Biology is an increasingly quantitative science. Thus, it is important that undergraduate biology curricula include frequent opportunities for students to practice their quantitative skills. This can create a substantial grading burden for faculty teaching online and/or large enrollment courses, but the "formula question" feature present in many learning management systems (LMS) offers a solution. Read More

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Lcapy: symbolic linear circuit analysis with Python.

Michael Hayes

PeerJ Comput Sci 2022 18;8:e875. Epub 2022 Feb 18.

Electrical and Computer Engineering, University of Canterbury, Christchchurch, New Zealand.

Lcapy is an open-source Python package for solving linear circuits symbolically. It uses a superposition of DC analysis, AC (phasor) analysis, transient (Laplace) analysis, and noise analysis. Expressions are evaluated using the computer algebra system SymPy. Read More

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February 2022

Realization of multi-configurable logic gate behaviour on fluorescence switching signalling of naphthalene diimide congeners.

RSC Adv 2021 Oct 1;11(56):35274-35279. Epub 2021 Nov 1.

Physical Sciences Division, Institute of Advanced Study in Science and Technology Paschim Boragaon Guwahati-781035 Assam India

Organic entities like suitably functionalized naphthalene diimide (NDI) exhibited logical behaviours in response to various external stimuli and can be used to develop digital logic operations. The present findings include utilization of two congeners of NDI , N1 and N2 for the successive turning ON/OFF of fluorescence with inclusion of acid and base. The recognition of the switching phenomenon of the probes N1 and N2 are applied to construct fundamental digital logic gates such as NOT, YES, IMPLICATION, INHIBIT, The inputs to each of the logic gates are defined by the presence or absence of acid and base. Read More

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October 2021

Research priorities to reduce the impact of COVID-19 in low- and middle-income countries.

J Glob Health 2022 15;12:09003. Epub 2022 Apr 15.

National Yang Ming Chiao Tung University, Taipei, Taiwan.

Background: The COVID-19 pandemic has caused disruptions to the functioning of societies and their health systems. Prior to the pandemic, health systems in low- and middle-income countries (LMIC) were particularly stretched and vulnerable. The International Society of Global Health (ISoGH) sought to systematically identify priorities for health research that would have the potential to reduce the impact of the COVID-19 pandemic in LMICs. Read More

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Swiss knife partial least squares (SKPLS): One tool for modelling single block, multiblock, multiway, multiway multiblock including multi-responses and meta information under the ROSA framework.

Anal Chim Acta 2022 May 30;1206:339786. Epub 2022 Mar 30.

Faculty of Science and Technology, Norwegian University of Life Sciences, 1430, Ås, Norway.

In the domain of chemometrics and multivariate data analysis, partial least squares (PLS) modelling is a widely used technique. PLS gains its beauty by handling the high collinearity found in multivariate data by replacing highly covarying variables with common subspaces spanned by orthogonal latent variables. Furthermore, all can be achieved with simple steps of linear algebra requiring minimal computation power and time usage compared to current high-end computing and substantial hyperparameter tuning required by methods such as deep learning. Read More

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Superachromatic polarization modulator for stable and complete polarization measurement over an ultra-wide spectral range.

Opt Express 2022 Apr;30(9):15113-15133

The polarization measurement system deals with polarized light-matter interactions, and has been a kind of powerful optical metrology applied in wide fields of physics and material. In this paper, we address several general theoretical aspects related to the system model and optimization for linear polarization systems from a view of the matrix algebra. Based on these theories, we propose a new framework of superachromatic polarization modulator (PM) by combining a linear polarizer and a sequence of parallel linear retarders (LRs) for a typical kind of linear polarization system based on the rotating compensator (RC) principle. Read More

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Brillouin Klein bottle from artificial gauge fields.

Nat Commun 2022 Apr 25;13(1):2215. Epub 2022 Apr 25.

National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing, 210093, China.

A Brillouin zone is the unit for the momentum space of a crystal. It is topologically a torus, and distinguishing whether a set of wave functions over the Brillouin torus can be smoothly deformed to another leads to the classification of various topological states of matter. Here, we show that under [Formula: see text] gauge fields, i. Read More

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Genomic Prediction of Complex Traits, Principles, Overview of Factors Affecting the Reliability of Genomic Prediction, and Algebra of the Reliability.

Methods Mol Biol 2022 ;2467:45-76

GenPhySE, Université de Toulouse, INRAE, ENVT, Castanet Tolosan, France.

The quality of the predictions of genetic values based on the genotyping of neutral markers (GEBVs) is a key information to decide whether or not to implement genomic selection. This quality depends on the part of the genetic variability captured by the markers and on the precision of the estimate of their effects. Selection index theory provided the framework for evaluating the accuracy of GEBVs once the information had been gathered, with the genomic relationship matrix (GRM) playing a central role. Read More

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Application of modular response analysis to medium- to large-size biological systems.

PLoS Comput Biol 2022 04 20;18(4):e1009312. Epub 2022 Apr 20.

Université de Montpellier, Montpellier, France.

The development of high-throughput genomic technologies associated with recent genetic perturbation techniques such as short hairpin RNA (shRNA), gene trapping, or gene editing (CRISPR/Cas9) has made it possible to obtain large perturbation data sets. These data sets are invaluable sources of information regarding the function of genes, and they offer unique opportunities to reverse engineer gene regulatory networks in specific cell types. Modular response analysis (MRA) is a well-accepted mathematical modeling method that is precisely aimed at such network inference tasks, but its use has been limited to rather small biological systems so far. Read More

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TurboBC: A Memory Efficient and Scalable GPU Based Betweenness Centrality Algorithm in the Language of Linear Algebra.

Proc Int Workshops Parallel Proc 2021 Aug 23;2021. Epub 2021 Sep 23.

School of Computing and Information Sciences, Florida, International University, Miami, Florida, USA.

Betweenness centrality (BC) is a shortest path centrality metric used to measure the influence of individual vertices or edges on huge graphs that are used for modeling and analysis of human brain, omics data, or social networks. The application of the BC algorithm to modern graphs must deal with the size of the graphs, as well with highly irregular data-access patterns. These challenges are particularly important when the BC algorithm is implemented on Graphics Processing Units (GPU), due to the limited global memory of these processors, as well as the decrease in performance due to the load unbalance resulting from processing irregular data structures. Read More

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Coordinating invisible and visible sameness within equivalence transformations of numerical equalities by 10- to 12-year-olds in their movement from computational to structural approaches.

ZDM 2022 Apr 9:1-13. Epub 2022 Apr 9.

Universidad de Colima, Colima, Mexico.

"They are the same" is a phrase that teachers often hear from their students in arithmetic and algebra. But what do students mean when they say this? The present paper researches the notion of sameness within algebraic thinking in the context of generating equivalent numerical equalities. A group of Grade 6 Mexican students (10- to 12-year-olds) was presented with tasks that required transforming the given numerical equalities in such a way as to show their truth-value. Read More

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Fast computation of matrix function-based centrality measures for layer-coupled multiplex networks.

Phys Rev E 2022 Mar;105(3-1):034305

Department of Mathematics, Technische Universität Chemnitz, 09107 Chemnitz, Germany.

Centrality measures identify and rank the most influential entities of complex networks. In this paper, we generalize matrix function-based centrality measures, which have been studied extensively for single-layer and temporal networks in recent years to layer-coupled multiplex networks. The layers of these networks can reflect different relationships and interactions between entities or changing interactions over time. Read More

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TurboBFS: GPU Based Breadth-First Search (BFS) Algorithms in the Language of Linear Algebra.

IEEE Int Symp Parallel Distrib Process Workshops Phd Forum 2021 Jun 24;2021:520-528. Epub 2021 Jun 24.

School of Computing and Information Sciences, Florida International University, Miami, Florida.

Graphs that are used for modeling of human brain, omics data, or social networks are huge, and manual inspection of these graph is impossible. A popular, and fundamental, method used for making sense of these large graphs is the well-known Breadth-First Search (BFS) algorithm. However, BFS suffers from large computational cost especially for big graphs of interest. Read More

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Geometric algebra generation of molecular surfaces.

J R Soc Interface 2022 Apr 13;19(189):20220117. Epub 2022 Apr 13.

Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA.

Geometric algebra is a powerful framework that unifies mathematics and physics. Since its revival in the 1960s, it has attracted great attention and has been exploited in fields like physics, computer science and engineering. This work introduces a geometric algebra method for the molecular surface generation that uses the Clifford-Fourier transform (CFT) which is a generalization of the classical Fourier transform. Read More

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Traffic-Data Recovery Using Geometric-Algebra-Based Generative Adversarial Network.

Sensors (Basel) 2022 Apr 2;22(7). Epub 2022 Apr 2.

Department of Transportation Information and Control Engineering, Tongji University, Shanghai 200092, China.

Traffic-data recovery plays an important role in traffic prediction, congestion judgment, road network planning and other fields. Complete and accurate traffic data help to find the laws contained in the data more efficiently and effectively. However, existing methods still have problems to cope with the case when large amounts of traffic data are missed. Read More

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Epistemic phase transitions in mathematical proofs.

Cognition 2022 Apr 8;225:105120. Epub 2022 Apr 8.

Social & Decision Sciences, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA; Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA. Electronic address:

Mathematical proofs are both paradigms of certainty and some of the most explicitly-justified arguments that we have in the cultural record. Their very explicitness, however, leads to a paradox, because the probability of error grows exponentially as the argument expands. When a mathematician encounters a proof, how does she come to believe it? Here we show that, under a cognitively-plausible belief formation mechanism combining deductive and abductive reasoning, belief in mathematical arguments can undergo what we call an epistemic phase transition: a dramatic and rapidly-propagating jump from uncertainty to near-complete confidence at reasonable levels of claim-to-claim error rates. Read More

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Study of normal-tension glaucoma based on OCTA and VBM-DARTEL analysis.

Exp Ther Med 2022 May 18;23(5):335. Epub 2022 Mar 18.

Department of Ophthalmology, The First Affiliated Hospital of Nanchang University, Jiangxi Branch of National Clinical Research Center for Ocular Disease, Nanchang, Jiangxi 330006, P.R. China.

The aim of the present study was to investigate the detection value of optical coherence tomography angiography (OCTA) and voxel-based morphometry with diffeomorphic anatomical registration through exponentiated lie algebra (VBM-DARTEL) in normal-tension glaucoma (NTG), as well as the correlation between the two functional indicators. A total of 30 patients (15 males, 15 females) with NTG and 30 (15 males, 15 females) age-, sex- and education-matched healthy controls underwent OCTA and 3.0 T MRI scanning. Read More

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The universal algebra of the electromagnetic field III. Static charges and emergence of gauge fields.

Lett Math Phys 2022 21;112(2):27. Epub 2022 Mar 21.

Dipartimento di Matematica, Universitá di Roma "Tor Vergata", Via della Ricerca Scientifica 1, 00133 Roma, Italy.

A universal C*-algebra of gauge invariant operators is presented, describing the electromagnetic field as well as operations creating pairs of static electric charges having opposite signs. Making use of Gauss' law, it is shown that the string-localized operators, which necessarily connect the charges, induce outer automorphisms of the algebra of the electromagnetic field. Thus they carry additional degrees of freedom which cannot be created by the field. Read More

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Kinematic Hopf Algebra for Bern-Carrasco-Johansson Numerators in Heavy-Mass Effective Field Theory and Yang-Mills Theory.

Phys Rev Lett 2022 Mar;128(12):121601

Centre for Theoretical Physics, Department of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom.

We present a closed formula for all Bern-Carrasco-Johansson (BCJ) numerators describing D-dimensional tree-level scattering amplitudes in a heavy-mass effective field theory with two massive particles and an arbitrary number of gluons. The corresponding gravitational amplitudes obtained via the double copy directly enter the computation of black-hole scattering and gravitational-wave emission. Our construction is based on finding a kinematic algebra for the numerators, which we relate to a quasishuffle Hopf algebra. Read More

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Frequency-domain analysis of fNIRS fluctuations induced by rhythmic mental arithmetic.

Psychophysiology 2022 Apr 8:e14063. Epub 2022 Apr 8.

Department of Physiology, Miguel Hernandez University, Alicante, Spain.

Functional near-infrared spectroscopy (fNIRS) is an increasingly used technology for imaging neural correlates of cognitive processes. However, fNIRS signals are commonly impaired by task-evoked and spontaneous hemodynamic oscillations of non-cerebral origin, a major challenge in fNIRS research. In an attempt to isolate the task-evoked cortical response, we investigated the coupling between hemodynamic changes arising from superficial and deep layers during mental effort. Read More

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The role of domain-general attention and domain-specific processing in working memory in algebraic performance: An experimental approach.

J Exp Psychol Learn Mem Cogn 2022 Mar;48(3):348-374

Department of Psychological Sciences.

We investigated the role of working memory in symbolic and spatial algebra and related tasks across five experiments. Each experiment combined a processing task (expression evaluation, arithmetic, coordinate plane, geometry, or mental rotation) with verbal and spatial memory loads in a dual-task design. Spatial memory was compromised in the presence of more difficult processing tasks, and verbal memory was only compromised in the presence of algebraic tasks. Read More

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